Augmenting the Unreturned for Field Data With Information on Returned Failures Only

Field data are an important source of reliability information for many commercial products. Because field data are often collected by the maintenance department, information on failed and returned units is well maintained. Nevertheless, information on unreturned units is generally unavailable. The unavailability leads to truncation in the lifetime data. This study proposes a data-augmentation algorithm for this type of truncated field return data with returned failures available only. The algorithm is based on an idea to reveal the hidden unobserved lifetimes. Theoretical justifications of the procedure for augmenting the hidden unobserved are given. On the other hand, the algorithm is iterative in nature. Asymptotic properties of the estimators from the iterations are investigated. Both point estimation and the information matrix of the parameters can be directly obtained from the algorithm. In addition, a by-product of the algorithm is a nonparametric estimator of the installation time distribution. An example from an asset-rich company is given to demonstrate the proposed methods. Supplementary materials for this article are available online.